The constraints of finite size in asexual populations and the rate of the ratchet

An analysis of mutation accumulation in finite, asexual populations shows that by modeling discrete individuals, a necessary condition for mutation-selection balance is often not met. It is found that over a wide parameter range (whenever N e(-mu/s) < 1, where N is the population size, mu is the genome-wide mutation rate, and s is the realized strength of selection), asexual populations will fail to achieve mutation-selection balance. This is specifically because the steady-state strength of selection on the best individuals is too weak to counter mutation pressure. The discrete nature of individuals means that if the equilibrium level of mutation and selection is such that less than one individual is expected in a class, then equilibration towards this level acts to remove the class. When applied to the classes with the fewest mutations, this drives mutation accumulation. This drive is in addition to the well-known identification of the stochastic loss of the best class as a mechanism for Muller's ratchet. Quantification of this process explains why the distribution of the number of mutations per individual can be markedly hypodispersed compared to the Poisson expectation. The actual distribution, when corrected for stochasticity between the best class and the mean, is akin to a shifted negative binomial. The parameterization of the distribution allows for an approximation for the rate of Muller's ratchet when N e(-mu/s) < 1. The analysis is extended to the case of variable selection coefficients where incoming mutations assume a distribution of deleterious effects. Under this condition, asexual populations accumulate mutations faster, yet may be able to survive longer, than previously estimated.